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By Christopher J. Foot

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Extra resources for ATMOSPHERIC THERMODYNAMICS - Elementary Physics and Chemistry

Sample text

Then the number of collisions per unit time (the collision frequency) is fcoll = n0 σc v [collision frequency]. 3) We may calculate the average distance between collisions to be the [distance per unit time] = [velocity] × [the time between collisions] (this last factor is the inverse of collision frequency): λ=v× 1 1 = n0 σc v n0 σc [mean free path, approximate form]. 4) The Greek letter λ is used in most texts to denote the mean free path. Actually, it is possible to solve the problem when all the particles are in motion, and the derivation can be found in books on the kinetic theory of gases.

3) In general, cv might be a function of temperature, but for an ideal gas it is not. For dry air the value of cv is 717 J kg−1 K−1 . In this process no work is done by the parcel on its environment, since the volume of the parcel does not change. All the heat given to the system goes into its internal energy. From the molecular relation 12 mv 2 = 32 kB T we recall that the average kinetic energy of the molecules is proportional to the Kelvin temperature. Hence, a change in internal energy is equivalent to a change in the kinetic energy (for an ideal monatomic gas).

3) In general, cv might be a function of temperature, but for an ideal gas it is not. For dry air the value of cv is 717 J kg−1 K−1 . In this process no work is done by the parcel on its environment, since the volume of the parcel does not change. All the heat given to the system goes into its internal energy. From the molecular relation 12 mv 2 = 32 kB T we recall that the average kinetic energy of the molecules is proportional to the Kelvin temperature. Hence, a change in internal energy is equivalent to a change in the kinetic energy (for an ideal monatomic gas).

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